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ModernSolarFacilities–AdvancedSolarScience,1–4 F.Kneer,K.G.Puschmann,A.D.Wittmann(eds.) (cid:13)c Universita¨tsverlagGo¨ttingen2007 Photospheric magnetic field and chromospheric emission R.Rezaei∗,R.Schlichenmaier,C.Beck,andW.Schmidt Kiepenheuer-Institutfu¨rSonnenphysik,Freiburg,Germany ∗Email: [email protected] 7 0 0 Abstract. Wepresentastatisticalanalysisofnetworkandinternetworkpropertiesinthephotosphere 2 andthechromosphere. Forthefirsttimewesimultaneouslyobserved(a)thefourStokesparametersof n thephotosphericironlinepairat630.2nmand(b)theintensityprofileoftheCaHlineat396.8nm. a Thevectormagneticfieldwasinferredfromtheinversionoftheironlines.Weaimatanunderstanding J ofthecouplingbetweenphotosphericmagneticfieldandchromosphericemission. 4 2 1 Observationsanddatareduction 1 v We observed a series of 13 maps of a network region and the surrounding quiet Sun at a 1 heliocentricangleof 53◦, closeto the activeregionNOAA 10675on September27, 2004, 8 with POLIS (Schmidtetal. 2003; Becketal. 2005) at the German VTT in Tenerife. The 6 Kiepenheuer Adaptive Optics System (KAOS) was used to improve spatial resolution to 1 about1arcsec(vonderLu¨heetal.2003). 0 7 Using theaverageprofile ofeachmap,wenormalized theintensityatthelinewingat 0 396.490nmtotheFTSprofile(Stenfloetal.1984). ¿FromtheintensityprofileofCaHwe / definelinepropertieslike,e.g.,theH-index,whichistheintegralaroundthelinecorefrom h p 396.8nmto396.9nm. Theseparationbetweennetworkandinternetworkisbasedon(i)the - mapsofmagneticfluxdensity,(ii)thepresenceofStokes-V signalsandemissioninCaH. o r t s 2 Inversion a : v An inversion was performed for the two iron lines at 630nm using the SIR code (Ruiz i Cobo & del Toro Iniesta 1992). To mimic unresolved magnetic fields, we used a model X atmospherewithonemagneticandonefield-freecomponent,plusstraylight.Theinversion r a yieldsamagneticfieldvector,aline-of-sightvelocity,andthemagneticfluxperpixel.These quantitiesareconstantalongthelineofsight.Usingthefluxdensitymaps,wecreatedamask toseparatenetworkandinternetworkregions. 3 Magneticfielddistribution The polarization signal in Q(λ), U(λ), and V(λ) is normalized by the local continuum in- tensity, I , for each pixel. The rms noise level of the Stokes parameters in the continuum c 2 R.Rezaeietal.: Photosphericmagneticfieldandchromosphericemission Figure1. Toptobuttom:thecontinuumintensitycloseto630nm,theH-index,andthemagneticflux densityobtainedfromtheinversion. 10 8 %) y( 6 c n e qu 4 e fr 2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 B (kG) Figure2.Distributionofthemagneticfieldstrengthforthenetwork(thick)andinternetwork(thin). was σ=8.0×10−4I forthe FeI630nmlines. Onlypixelswith V signalsgreaterthan3σ c wereincludedintheprofileanalysis.Weobtainamagneticfielddistributionwhichpeaksat some1.4kGforthenetworkelementsandatabout200G fortheinternetworkelementsin agreementwithpreviousinfraredobservations,butincontradictionwithresultsfromvisible lines(Collados2001;Lites2002). 3.1 Theeffectofnoiseintheweak-fieldlimit Ourfindingofweakratherthanstrongfieldscanbeexplainedbythehighspatialresolution andhighpolarimetricaccuracythatwehaveachievedinourmeasurements. Sincetheinter- networkmagneticfieldsareintheweak-fieldlimit,theamountofnoisestronglyinfluences R.Rezaeietal.:Photosphericmagneticfieldandchromosphericemission 3 1 Figure3.Theleft(right)fourpanelsshowtheinversionresultsoftheoriginal(noisy)data. 18 14 13 16 12 m) m) x (p 14 x (p 11 e e nd 12 nd 10 H-i H-i 9 10 8 8 7 50 100 150 200 250 300 0 10 20 30 40 50 abs flux density (Mx cm-2) abs flux density (Mx cm-2) Figure 4. TheH-indexvs. themagneticfluxdensityinthenetwork(left)andinternetwork(right). Black squares show the binned data. The curves show the fit to the original data along with 1σ confidencelevel. theoutcomeoftheinversion.Figure3showstwodifferentcases: 1. AfitofanoriginalsetofStokesprofilesyieldsB=840Gwithafillingfactorof7.6% (leftpanel,Fig. 3). 2. A fit on the same profile with addednoise (such that the rms noise levelis twice as large)deliversB=1.5kGandafillingfactorofonly5.3%(rightfourpanels,Fig. 3). The reduction of noise and improvement of spatial resolution may resolve the existing discrepancybetweenvisibleandinfraredmagneticfieldmeasurements. 4 TheH-indexvs. magneticfluxdensity The left panel of Fig. 4 shows the H-index versus photosphericmagnetic flux, Φ, for the network.Apowerlawfit,H =a Φb+c,yieldsb=0.3andc=10pm.Intheinternetworkthe H-indexdoesnotcorrelatewiththemagneticfluxdensity(Fig. 4,rightpanel). Theaverage valueoftheH-indexintheinternetworkisaboutH=10pm.Theoffsetvalue,c=10pm,can beinterpretedasthenon-magneticheatingcontributionandthestraylight. For the first time the H-index and simulaneously measured V-profile parameters can be compared. We find no correlation between these parameters in the internetwork (Fig. 5, 4 R.Rezaeietal.: Photosphericmagneticfieldandchromosphericemission 14 14 13 13 m) m) p 12 p 12 x ( 11 x ( 11 e e d d n 10 n 10 H-i 9 H-i 9 8 8 -60 -40 -20 0 20 40 60 -3 -2 -1 0 1 2 3 area asymmetry (%) Fe 630.25 V velocity (km/s) Figure5.ScatterplotoftheareaasymmetryandStokes-VvelocityagainsttheH-index. pluses). Inthenetwork,acorrelationexists,andtheH-indexpeaksatasmallpositivevalue fortheareaasymmetryandatvanishingV-profileDopplershift(Fig. 5,squares). 5 Conclusions •Theinternetworkmagneticfielddistributionpeaksaround200Ganditsmeanabsoluteflux densityamountsto9Mxcm−2.Thefindingofweakratherthanstrongfieldsisaconsequence ofthehighspatialresolutionandhighpolarimetricaccuracy. •TheH-indexinthenetworkiscorrelatedtothemagneticfluxdensity,approachingavalue ofH=10pmforvanishingflux. • The H-index in the internetwork is not correlated to any property of the photospheric magnetic field implying that the chromospheric brightenings in the internetwork are non- magnetic. • For high values of the H-index, the network shows small positive area (and amplitude) asymmetry,beingconsistentwiththescenarioofaline-of-sightcrossingthemagneticbound- ary(canopy)offluxtubesthatfansoutwithheight(Steiner1999). 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